My understanding is that Picts were a insular culture indigenous to Scotland, and were a separate people from the Gaels, Britons, Romano-Britons, Norsemen, and Anglo-Saxons who were their neighbors at the time. My question is, why was it that it was the Gaels (who were actually foreign invaders to the island of Great Britain like the Norsemen and Anglo-Saxons) who were able to successfully assimilate them and not the other groups?
The successful Gaelicization is based off historical accounts that the Gaelic arrivals/invaders who planted themselves in western Scotland were able to unite with the Pictish kingdoms to form the powerful Kingdom of Alba. This polity that was so thoroughly Gaelicized that the population in a short time span had completely forgotten their Pictish past and considered themselves as fully Gaelic.
I'm not completely up-to-date on this topic, since it's not been my primary interest for a number of years. That said, however, linguistic evidence strongly suggests that the Picts were Britons. They are ethno-linguistically related to other speakers of the P-Celtic dialects, the modern survivors of which are Welsh, Cornish, and Breton. Thus the Picts are in turn pretty closely related linguistically and ethnically to Gaels, who speak Q-Celtic dialects. There was always a lot of cultural contact between the largely P-Celtic Britons and their Q-Celtic neighbors to the west. At various times, at least according to medieval Irish annals, some Pictish tribes even inhabited Ireland. Britons and Gaels intermarried and traded, and because their political elites intermarried, the ruling classes were even more closely related than their people. This is why Cináed mac Alpín (Kenneth mac Alpine), nominally a Gael, was able to assume kingship of Pictland in 842. Furthermore, the Britons and Gaels were converted to Christianity before the Anglo-Saxon or Norse peoples, which created another cultural bond that facilitated the eventual assimilation of the Picts. Under pressure from non-Christian invaders, the various Celtic peoples were, one could say, driven further into one another's arms, and a smaller number of stronger kingdoms emerged. The Gaelicization of the Pictish population was thus the product of centuries of gradual assimilation. Now, why it should have been the more numerous Picts who were Gaelicized rather than the Irish Gaels "Britonized" is a good and valid question that I'm not sure would have any clear answer. There are lots of historical examples of foreign elites eventually adopting the language of the subject people, as in the case of the (Germanic) Franks adopting the local version of vulgar Latin eventually, i.e. French. Then again, the Picts were not really "subject" to the Gaels but instead fused with them.
Source: Michael Newton, A Handbook of the Scottish Gaelic World, 2000